Simplify the following expression: $k = \dfrac{4a}{7} + \dfrac{3a}{4}$
Solution: In order to add expressions, they must have a common denominator. The smallest common denominator is the least common multiple of $7$ and $4$ $\lcm(7, 4) = 28$ $ k = \dfrac{4}{4} \cdot \dfrac{4a}{7} + \dfrac{7}{7} \cdot \dfrac{3a}{4} $ $k = \dfrac{16a}{28} + \dfrac{21a}{28}$ $k = \dfrac{16a +21a}{28}$ $k = \dfrac{37a}{28}$